Q1. A system is taken through a series of processes as a result of which it is restored to the initial state. The work and heat interactions for some of the processes are measured and they are as given below:

Complete the table (i.e., fill in the gaps marked by ?) and determine the net work done and net heat interaction.

Q2. A mass m of liquid at temperature T1 is mixed with an equal amount of the same liquid at temperature T2. Show that the total entropy change because of this mixing is:

Δs = 2mCpln((T₁ + T₂)/2/√T₁T₂)

ΔS = 2mC_pin 

If temperatures T1 and T2 were 25^°C and 75^°C respectively for 2 kg of each liquid, then calculate ΔS. Specific heat (C_r) for this liquid is 4.184 kJ kg^-1K^-1.

Q3. Heat capacities C_v and C_p are defined as temperature derivatives respectively of U and H. Because these properties are related, one expects the heat capacities also to be related. Using the relationship of S to the heat capacities, or otherwise, show that the general expression connecting C_p to C_v is:

C_p - C_v = TVβ/k²

Q4 A mixture of CO(g) and H₂0(g) in the mole ratio 1:4 enters a reactor which is maintained at 100 bar and 1000K. The CO(g) and H₂0(g) react according to the equation

CO(g) + H₂0(g) --> CO₂(g) + H₂(g)

The equilibrium constant for this reaction at 1000K is 3. Assuming that the reaction mixture behaves like an ideal gas, determine the degree of conversion of CO(g).

Q5 For the system methanol(1)/methyl acetate(2), the following equations provide a reasonable correlation for the activity coefficients:

Iny₁ = Ax₂²         Iny₂= Ax₁²       where A = 2.771 - 0.00523T

In addition, the following Antoine equations provide vapour pressures:

In p₁^sat = 16.59158 - 3643.31/T-33.424

In P₂^sat = 14.25326 - 2665.54/T-53.424

where T in kelvins and the vapour pressures are in kPa.

Calculate P and {x_i}for T= 370 K and y₁= 0.70. Give your answer to P in kPa to 1 decimal place, and x_i, x₂ to 3 decimal places.